Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation

TL;DR

This paper derives analytical breather solutions for a 3D nonlinear Gross-Pitaevskii equation, demonstrating how variable coefficients can modulate breather excitations, with potential applications in Bose-Einstein condensates.

Contribution

It introduces a method to reduce a 3D nonlinear equation with variable coefficients to a 1D form, enabling analytical breather solutions and modulation control.

Findings

Analytical breather solutions for the 3D Gross-Pitaevskii equation.

Variable coefficients can modulate breather excitations.

Discussion on experimental feasibility in Bose-Einstein condensates.

Abstract

In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into an one-dimensional equation with constant coefficients. The key point is to show that both the space- and time-dependent coefficients of the nonlinear equation can contribute to modulate the breather excitations. We briefly discuss the experimental feasibility of the results in Bose-Einstein condensates.